Such a move would be a blow to President Hassan Rouhani, who had hoped the prestigious project could make other international businesses regain confidence in Iran and bring in investment.
"It's a bad sign. The EU can't compel or really protect the private sector," Sanam Vakil, associate fellow at Chatham House, said of Total's announcement.
Trump's decision to abandon the 2015 nuclear accord risks exposing European countries that have since invested in Iran to renewed U.S. sanctions, after "wind-down" periods of three to six months expire.
Danish oil product shipping operator Maersk Tankers said it would wind down its customer agreements in Iran by November, while German insurer Allianz said on Tuesday it was preparing to wind down Iran-related business.
The 28 EU leaders meeting in Sofia did not make any quick decisions on how to try to shield their economic cooperation with Iran.
European Commission head Jean-Claude Juncker presented options to protect European investment, which include retaliatory sanctions, allowing the European Investment Bank to invest in Iran, and coordinating euro-denominated credit lines from European governments.
But the reach of the U.S. financial system, the dominance of the dollar and the presence of European companies' operations in the United States all weaken any potential EU measures.
Iran has said it may start enriching uranium again if it can no longer see any economic benefit from sticking to the deal, which lifted earlier international sanctions on the Islamic Republic in exchange for it curbing its nuclear ambitions.
British, French and German foreign ministers vowed to try to keep Iran's oil and investment flowing after a meeting with their Iranian counterpart on Tuesday but admitted they would struggle to provide the guarantees Tehran seeks.
They tasked experts with coming up with measures for a meeting of their deputies in Vienna next week.
The EU's top energy official, Commissioner Miguel Arias Canete, is meanwhile heading to Iran on May 18-21 for talks on energy cooperation, a symbolic gesture from the EU that it wants to stay engaged despite the U.S. withdrawal.
"WHO NEEDS ENEMIES?"
Total said it would wind down operations linked to the South Pars gas venture before Nov. 4 unless it were granted a specific project waiver by the U.S. authorities, with the support of the French and European authorities.
The French firm signed a deal with Tehran in July 2017 to develop phase 11 of Iran's South Pars field, marking the first major Western energy investment in the long isolated country since the lifting of sanctions.
Underlining the depth of trans-Atlantic discord, the chairman of EU leaders Donald Tusk said Trump had "rid Europe of all illusions" by withdrawing from the Iran accord and driving trade disputes.
"Looking at the latest decisions of President Trump, someone could even think: With friends like that, who needs enemies?" Tusk told a news conference.
Repudiating the result of more than a decade of diplomacy, Trump quit the accord last week, complaining that the deal does not cover Iran's ballistic missiles, its role in regional wars or what happens after the pact begins to expire in 2025.
Major European countries share Trump's concerns, and the EU leaders on Wednesday agreed to seek ways to address them. But they argue that the nuclear deal is the way to stop the increasingly influential regional power from obtaining an atomic weapon.
German Chancellor Angela Merkel insisted the pact also helped with concerns about Tehran's role in Middle East conflicts.
"The question is whether you can talk better if you terminate an agreement or if you stay in it ... we say you can talk better if you remain in it," she told the Bundestag, the lower house of parliament..
In Moscow, Deputy Foreign Minister Sergei Ryabkov said Russia supported an EU proposal to hold a meeting on the Iran deal in Vienna, Interfax news agency said. The meeting is due on May 25.
The United States imposed sanctions on Tuesday on Iran's central bank governor, three other individuals, and an Iraqi-based bank as Washington seeks to cut off funding it says Tehran is using to fund militant activities overseas.
Iran said the new U.S. sanctions were an attempt to derail efforts to save the nuclear deal.
Rouhani said Trump had expected Iran to leave the deal after the U.S. withdrawal, but Tehran had refused to follow that plan by trying to save the deal with its remaining signatories.
"Trump played his first card, but miscalculated the second move," Rouhani was quoted as saying by the ISNA agency. (Additional reporting by Bozorgmehr Sharafedin in London, Sudip Kar-Gupta in Paris, Michelle Martin in Berlin, Writing by William Maclean; Editing by Jon Boyle, Nick Tattersall and Cynthia Osterman)
© Reuters News 2018